Moment-preserving spline approximation and Turán quadratures. (English) Zbl 0659.65010

Milovanović, Gradimir V.; Kovačević, Milan A.

Numerical mathematics, Proc. Int. Conf., Singapore 1988, ISNM, Int. Ser. Numer. Math. 86, 357-365 (1988).

Authors’ summary: [For the entire collection see Zbl 0644.00018.]
We consider the problem of approximating a function f of the radial distance r in \({\mathbb{R}}^ d\) on \(0\leq r<\infty\) by a spline function of degree m and defect k, with n (variable) knots, matching as many of the initial moments of f as possible. We analyse the case when the defect k is an odd integer, especially when \(k=3\). We show that, if the approximation exists, it can be represented in terms of generalized Turán quadrature relative to a measure depending on f. The knots of the spline are the zeros of the corresponding s-orthogonal polynomials (s\(\geq 1)\). Numerical example is included.

Reviewer: J.N.Lyness

MSC:

65D15	Algorithms for approximation of functions
65D07	Numerical computation using splines
41A15	Spline approximation

Keywords:

moment-preserving spline approximation; Turán quadrature; orthogonal polynomials; Numerical example